DOCSLIB.ORG

Model Checking CTL Is Almost Always Inherently Sequential

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Model Checking CTL Is Almost Always Inherently Sequential This is a repository copy of Model Checking CTL is Almost Always Inherently Sequential. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/74808/ Proceedings Paper: Beyersdorff, O, Meier, A, Thomas, M et al. (3 more authors) (2009) Model Checking CTL is Almost Always Inherently Sequential. In: Lutz, C and Raskin, J-F, (eds.) 16th International Symposium on Temporal Representation and Reasoning 2009. International Symposium on Temporal Representation and Reasoning, 23 - 25 July 2009, Bressanone, Brixen, Italy. IEEE , 21 - 28 . ISBN 978-0-7695-3727-6 https://doi.org/10.1109/TIME.2009.12 Reuse See Attached Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ Model Checking CTL is Almost Always Inherently Sequential∗ Olaf Beyersdorff Arne Meier Michael Thomas Heribert Vollmer Theoretical Computer Science, University of Hannover, Germany {beyersdorff, meier, thomas, vollmer}@thi.uni-hannover.de Martin Mundhenk Computer Science, University of Jena, Germany [email protected] Thomas Schneider Computer Science, University of Manchester, UK [email protected] Abstract of another event (R), as well as path quantifiers (E, A) for speaking about computation paths. The full language ob- The model checking problem for CTL is known to be tained by these operators and quantifiers is called CTL⋆ [5]. P-complete (Clarke, Emerson, and Sistla (1986), see Schnoe- In CTL, the interaction between the temporal operators and belen (2002)). We consider fragments of CTL obtained path quantifiers is restricted. The temporal operators in CTL by restricting the use of temporal modalities or the use of are obtained by path quantifiers followed directly by any negations—restrictions already studied for LTL by Sistla and temporal operator, e.g., AF and AU are CTL-operators. Be- Clarke (1985) and Markey (2004). For all these fragments, cause they start with the universal path quantifier, they are except for the trivial case without any temporal operator, we called universal CTL-operators. Accordingly, EX and EG systematically prove model checking to be either inherently are examples for existential CTL-operators. sequential (P-complete) or very efficiently parallelizable Since properties are largely verified automatically, the (LOGCFL-complete). For most fragments, however, model computational complexity of reasoning tasks is of great in- checking for CTL is already P-complete. Hence our results terest. Model checking (MC)—the problem of verifying indicate that in most applications, approaching CTL model whether a given formula holds in a state of a given model— checking by parallelism will not result in the desired speed is one of the most important reasoning tasks [15]. It is in- up. tractable for CTL⋆ (PSPACE-complete [6, 15]), but tractable We also completely determine the complexity of the model for CTL (solvable in, and even hard for, polynomial time checking problem for all fragments of the extensions ECTL, [3, 15]). CTL+, and ECTL+. Although model checking for CTL is tractable, its P- hardness means that it is presumably not efficiently paral- lelizable. We therefore search for fragments of CTL with 1. Introduction a model checking problem of lower complexity. We will consider all subsets of CTL-operators, and examine the com- Temporal logic was introduced by Pnueli [12] as a formal- plexity of the model checking problems for all resulting ism to specify and verify properties of concurrent programs. fragments of CTL. Further, we consider three additional Computation Tree Logic (CTL), the logic of branching time, restrictions affecting the use of negation and study the exten- goes back to Emerson and Clarke [4] and contains tempo- sions ECTL, CTL+, and their combination ECTL+. ral operators for expressing that an event occurs at some The complexity of model checking for fragments of tem- time in the future (F), always in the future (G), in the next poral logics has been examined in the literature: Markey [9] point of time (X), always in the future until another event considered satisfiability and model checking for fragments of holds (U), or as long as it is not released by the occurrence Linear Temporal Logic (LTL). Under systematic restrictions ∗Supported in part by grants DFG VO 630/6-1 and DAAD-ARC to the temporal operators, the use of negation, and the inter- D/08/08881. action of future and past operators, Markey classified the two 1 decision problems into NP-complete, coNP-complete, and ⊥, the Boolean connectives ¬, ∧, and ∨, and the temporal PSPACE-complete. Further, [1] examined model checking operator symbols A, E, X, F, G, U, and R. for all fragments of LTL obtained by restricting the set of A and E are called a path quantifiers, temporal operators temporal and propositional operators. The resulting classi- aside from A and E are pure temporal operators. The atomic fication separated cases where model checking is tractable propositions and the constants ⊤ and ⊥ are atomic formulae. from those where it is intractable. There are two kinds of formulae, state formulae and path Concerning CTL and its extension ECTL, our results in formulae. Each atomic formula is a state formula, and each this paper show that most restricted versions of the model state formula is a path formula. If ϕ, ψ are state formulae checking problem exhibit the same hardness as the general and χ, π are path formulae, then ¬ϕ, (ϕ ∧ ψ), (ϕ ∨ ψ), problem. More precisely, we show that apart from the trivial Aχ, Eχ are state formulae, and ¬χ, (χ ∧ π), (χ ∨ π), Xχ, case where CTL-operators are completely absent, the com- Fχ, Gχ, [χUπ], and [χRπ] are path formulae. The set of plexity of CTL model checking is a dichotomy: it is either CTL⋆-formulae (or formulae) consists of all state formulae. P-complete or LOGCFL-complete. Unfortunately, the latter A Kripke structure is a triple K = (W, R, η), where W case only occurs for a few rather weak fragments and hence is a finite set of states, R ⊆ W × W a total relation (i. e., for there is not much hope that in practice, model checking can each w ∈ W , there exists a w′ such that (w, w′) ∈ R), and be sped up by using parallelism—it is inherently sequential. η : W → P(Φ) is a labelling function. A path x is an infinite ω Put as a simple rule, model checking for CTL is P- sequence x = (x1, x2,...) ∈ W such that (xi, xi+1) ∈ R, i complete for every fragment that allows to express a uni- for all i ≥ 1. For a path x = (x1, x2,...) we denote by x versal and an existential CTL-operator. Only for fragments the path (xi, xi+1,...). involving the operators EX and EF (or alternatively AX and Let K = (W, R, η) be a Kripke structure, w ∈ W be a ω AG) model checking is LOGCFL-complete. This is visual- state, and x = (x1, x2,... ) ∈ W be a path. Further, let ized in Fig. 2 in Sect. 5. Recall that LOGCFL is defined ϕ, ψ be state formulae and χ, π be path formulae. The truth as the class of problems logspace-reducible to context-free of a CTL⋆-formula w. r. t. K is inductively defined as: languages, and NL ⊆ LOGCFL ⊆ NC2 ⊆ P. Hence, in contrast to inherently sequential P-hard tasks, problems in K, w |= ⊤ always, LOGCFL have very efficient parallel algorithms. K, w |= ⊥ never, For the extensions CTL+ and ECTL+, the situation is K, w |= p iff p ∈ Φ and p ∈ η(w), more complex. In general, model checking CTL+ and K, w |= ¬ϕ iff K, w 6|= ϕ, + p K, w ϕ ψ iff K, w ϕ and K, w ψ, ECTL is ∆ -complete [8]. We show that for T ⊆ |= ( ∧ ) |= |= 2 K, w ϕ ψ iff K, w ϕ or K, w ψ, {A, E, X}, both model checking problems remain tractable, |= ( ∨ ) |= |= A E X p K, w |= Aχ iff K, x |= χ for all paths while for T * { , , }, both problems become ∆2- complete. Yet, for negation restricted fragments with only x = (x1, x2,...) with x1 = w, existential or only universal path quantifiers, we observe a K, x |= ϕ iff K, x1|= ϕ, complexity decrease to NP- resp. coNP-completeness. K, x |= ¬χ iff K, x 6|= χ, K, x |= (χ ∧ π) iff K, x |= χ and K, x |= π, This paper is organized as follows: Section 2 introduces K, x |= (χ ∨ π) iff K, x |= χ or K, x |= π, CTL, its model checking problems, and the non-basics of K, x |= Xχ iff K, x2|= χ complexity theory we use. Section 3 contains our main K, x |= [χUπ] iff there exists k ∈ such that results, separated into upper and lower bounds. We also N K, xi |= χ for 1 ≤ i < k and provide a refined analysis of the reductions between different K, xk |= π. model checking problems with restricted use of negation. The results are then generalized to extensions of CTL in The semantics of the remaining temporal operators is Section 4. Finally, Section 5 concludes with a graphical defined via the equivalences: Eχ ≡ ¬A¬χ, Fχ ≡ [⊤Uχ], overview of the results. For brevity, some proofs are omitted Gχ ≡ ¬F¬χ, and [χRπ] ≡ ¬[¬χU¬π]. A state formula ϕ and will be included in the full version of this paper. is satisfied by a Kripke structure K if there exists w ∈ W such that K, w |= ϕ. We will also denoted this by K |= ϕ. ⋆ 2. Preliminaries A CTL-formula is a CTL -formula in which each path quantifier is followed by exactly one pure temporal operator and each pure temporal operator is preceded by exactly one 2.1.
Load more

Recommended publications
  • Model Checking
    Lecture 1: Model Checking Edmund Clarke School of Computer Science Carnegie Mellon University 1 Cost of Software Errors June 2002 “Software bugs, or errors, are so prevalent and so detrimental that they cost the U.S. economy an estimated $59.5 billion annually, or about 0.6 percent of the gross domestic product … At the national level, over half of the costs are borne by software users and the remainder by software developers/vendors.” NIST Planning Report 02-3 The Economic Impacts of Inadequate Infrastructure for Software Testing 2 Cost of Software Errors “The study also found that, although all errors cannot be removed, more than a third of these costs, or an estimated $22.2 billion, could be eliminated by an improved testing infrastructure that enables earlier and more effective identification and removal of software defects.” 3 Model Checking • Developed independently by Clarke and Emerson and by Queille and Sifakis in early 1980’s. • Properties are written in propositional temporal logic. • Systems are modeled by finite state machines. • Verification procedure is an exhaustive search of the state space of the design. • Model checking complements testing/simulation. 4 Advantages of Model Checking • No proofs!!! • Fast (compared to other rigorous methods) • Diagnostic counterexamples • No problem with partial specifications / properties • Logics can easily express many concurrency properties 5 Model of computation Microwave Oven Example State-transition graph describes system evolving ~ Start ~ Close over time. ~ Heat st ~ Error Start ~ Start ~ Start ~ Close Close Close ~ Heat Heat ~ Heat Error ~ Error ~ Error Start Start Start Close Close Close ~ Heat ~ Heat Heat Error ~ Error ~ Error 6 Temporal Logic l The oven doesn’t heat up until the door is closed.
    [Show full text]
  • Model Checking TLA Specifications
    Model Checking TLA+ Specifications Yuan Yu1, Panagiotis Manolios2, and Leslie Lamport1 1 Compaq Systems Research Center {yuanyu,lamport}@pa.dec.com 2 Department of Computer Sciences, University of Texas at Austin [email protected] Abstract. TLA+ is a specification language for concurrent and reac- tive systems that combines the temporal logic TLA with full first-order logic and ZF set theory. TLC is a new model checker for debugging a TLA+ specification by checking invariance properties of a finite-state model of the specification. It accepts a subclass of TLA+ specifications that should include most descriptions of real system designs. It has been used by engineers to find errors in the cache coherence protocol for a new Compaq multiprocessor. We describe TLA+ specifications and their TLC models, how TLC works, and our experience using it. 1 Introduction Model checkers are usually judged by the size of system they can handle and the class of properties they can check [3,16,4]. The system is generally described in either a hardware-description language or a language tailored to the needs of the model checker. The criteria that inspired the model checker TLC are completely different. TLC checks specifications written in TLA+, a rich language with a well-defined semantics that was designed for expressiveness and ease of formal reasoning, not model checking. Two main goals led us to this approach: – The systems that interest us are too large and complicated to be completely verified by model checking; they may contain errors that can be found only by formal reasoning. We want to apply a model checker to finite-state models of the high-level design, both to catch simple design errors and to help us write a proof.
    [Show full text]
  • Introduction to Model Checking and Temporal Logic¹
    Formal Verification Lecture 1: Introduction to Model Checking and Temporal Logic¹ Jacques Fleuriot [email protected] ¹Acknowledgement: Adapted from original material by Paul Jackson, including some additions by Bob Atkey. I Describe formally a specification that we desire the model to satisfy I Check the model satisfies the specification I theorem proving (usually interactive but not necessarily) I Model checking Formal Verification (in a nutshell) I Create a formal model of some system of interest I Hardware I Communication protocol I Software, esp. concurrent software I Check the model satisfies the specification I theorem proving (usually interactive but not necessarily) I Model checking Formal Verification (in a nutshell) I Create a formal model of some system of interest I Hardware I Communication protocol I Software, esp. concurrent software I Describe formally a specification that we desire the model to satisfy Formal Verification (in a nutshell) I Create a formal model of some system of interest I Hardware I Communication protocol I Software, esp. concurrent software I Describe formally a specification that we desire the model to satisfy I Check the model satisfies the specification I theorem proving (usually interactive but not necessarily) I Model checking Introduction to Model Checking I Specifications as Formulas, Programs as Models I Programs are abstracted as Finite State Machines I Formulas are in Temporal Logic 1. For a fixed ϕ, is M j= ϕ true for all M? I Validity of ϕ I This can be done via proof in a theorem prover e.g. Isabelle. 2. For a fixed ϕ, is M j= ϕ true for some M? I Satisfiability 3.
    [Show full text]
  • Model Checking and the Curse of Dimensionality
    Model Checking and the Curse of Dimensionality Edmund M. Clarke School of Computer Science Carnegie Mellon University Turing's Quote on Program Verification . “How can one check a routine in the sense of making sure that it is right?” . “The programmer should make a number of definite assertions which can be checked individually, and from which the correctness of the whole program easily follows.” Quote by A. M. Turing on 24 June 1949 at the inaugural conference of the EDSAC computer at the Mathematical Laboratory, Cambridge. 3 Temporal Logic Model Checking . Model checking is an automatic verification technique for finite state concurrent systems. Developed independently by Clarke and Emerson and by Queille and Sifakis in early 1980’s. The assertions written as formulas in propositional temporal logic. (Pnueli 77) . Verification procedure is algorithmic rather than deductive in nature. 4 Main Disadvantage Curse of Dimensionality: “In view of all that we have said in the foregoing sections, the many obstacles we appear to have surmounted, what casts the pall over our victory celebration? It is the curse of dimensionality, a malediction that has plagued the scientist from the earliest days.” Richard E. Bellman. Adaptive Control Processes: A Guided Tour. Princeton University Press, 1961. Image courtesy Time Inc. 6 Photographer Alfred Eisenstaedt. Main Disadvantage (Cont.) Curse of Dimensionality: 0,0 0,1 1,0 1,1 2-bit counter n-bit counter has 2n states 7 Main Disadvantage (Cont.) 1 a 2 | b n states, m processes | 3 c 1,a nm states 2,a 1,b 3,a 2,b 1,c 3,b 2,c 3,c 8 Main Disadvantage (Cont.) Curse of Dimensionality: The number of states in a system grows exponentially with its dimensionality (i.e.
    [Show full text]
  • Formal Verification, Model Checking
    Introduction Modeling Specification Algorithms Conclusions Formal Verification, Model Checking Radek Pel´anek Introduction Modeling Specification Algorithms Conclusions Motivation Formal Methods: Motivation examples of what can go wrong { first lecture non-intuitiveness of concurrency (particularly with shared resources) mutual exclusion adding puzzle Introduction Modeling Specification Algorithms Conclusions Motivation Formal Methods Formal Methods `Formal Methods' refers to mathematically rigorous techniques and tools for specification design verification of software and hardware systems. Introduction Modeling Specification Algorithms Conclusions Motivation Formal Verification Formal Verification Formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property. Introduction Modeling Specification Algorithms Conclusions Motivation Formal Verification vs Testing formal verification testing finding bugs medium good proving correctness good - cost high small Introduction Modeling Specification Algorithms Conclusions Motivation Types of Bugs likely rare harmless testing not important catastrophic testing, FVFV Introduction Modeling Specification Algorithms Conclusions Motivation Formal Verification Techniques manual human tries to produce a proof of correctness semi-automatic theorem proving automatic algorithm takes a model (program) and a property; decides whether the model satisfies the property We focus on automatic techniques. Introduction Modeling Specification Algorithms Conclusions
    [Show full text]
  • Formal Verification of Diagnosability Via Symbolic Model Checking
    Formal Verification of Diagnosability via Symbolic Model Checking Alessandro Cimatti Charles Pecheur Roberto Cavada ITC-irst RIACS/NASA Ames Research Center ITC-irst Povo, Trento, Italy Moffett Field, CA, U.S.A. Povo, Trento, Italy mailto:[email protected] [email protected] [email protected] Abstract observed system. We propose a new, practical approach to the verification of diagnosability, making the following contribu• This paper addresses the formal verification of di• tions. First, we provide a formal characterization of diagnos• agnosis systems. We tackle the problem of diagnos• ability problem, using the idea of context, that explicitly takes ability: given a partially observable dynamic sys• into account the run-time conditions under which it should be tem, and a diagnosis system observing its evolution possible to acquire certain information. over time, we discuss how to verify (at design time) Second, we show that a diagnosability condition for a given if the diagnosis system will be able to infer (at run• plant is violated if and only if a critical pair can be found. A time) the required information on the hidden part of critical pair is a pair of executions that are indistinguishable the dynamic state. We tackle the problem by look• (i.e. share the same inputs and outputs), but hide conditions ing for pairs of scenarios that are observationally that should be distinguished (for instance, to prevent simple indistinguishable, but lead to situations that are re• failures to stay undetected and degenerate into catastrophic quired to be distinguished. We reduce the problem events). We define the coupled twin model of the plant, and to a model checking problem.
    [Show full text]
  • ACM 2007 Turing Award Edmund Clarke, Allen Emerson, and Joseph Sifakis Model Checking: Algorithmic Verification and Debugging
    ACM 2007 Turing Award Edmund Clarke, Allen Emerson, and Joseph Sifakis Model Checking: Algorithmic Verification and Debugging ACM Turing Award Citation precisely describe what constitutes correct behavior. This In 1981, Edmund M. Clarke and E. Allen Emerson, work- makes it possible to contemplate mathematically establish- ing in the USA, and Joseph Sifakis working independently ing that the program behavior conforms to the correctness in France, authored seminal papers that founded what has specification. In most early work, this entailed constructing become the highly successful field of Model Checking. This a formal proof of correctness. In contradistinction, Model verification technology provides an algorithmic means of de- Checking avoids proofs. termining whether an abstract model|representing, for ex- ample, a hardware or software design|satisfies a formal Hoare-style verification was the prevailing mode of formal specification expressed as a temporal logic formula. More- verification going back from the late-1960s until the 1980s. over, if the property does not hold, the method identifies This classic and elegant approach entailed manual proof con- a counterexample execution that shows the source of the struction, using axioms and inference rules in a formal de- problem. ductive system, oriented toward sequential programs. Such proof construction was tedious, difficult, and required hu- The progression of Model Checking to the point where it man ingenuity. This field was a great academic success, can be successfully used for complex systems has required spawning work on compositional or modular proof systems, the development of sophisticated means of coping with what soundness of program proof systems, and their completeness; is known as the state explosion problem.
    [Show full text]
  • Introduction to Model-Checking Theory and Practice
    Introduction to Model-Checking Theory and Practice Beihang International Summer School 2018 Model Checking Linear Temporal Properties Model Checking “Model checking is the method by which a desired behavioral property of a reactive system is verified over a given system (the model) through exhaustive enumeration (explicit or implicit ) of all the states reachable by the system and the behaviors that traverse through them” Amir Pnueli (2000) Basic Properties • reachability (something is possible) • invariant (something is always true) the gate is closed when the train cross the road • safety (something bad never happen: ≡ ¬ 푅푒푎푐ℎ) • liveness (something good may eventually happen) every process will (eventually) gain access to the printer • Fairness (if it may happen ∞ often then it will happen) if messages cannot be lost ∞ often then I will received an ack Model-Checking • We have seen how to use a formal specification language to model the system (⇒ as a graph, but also as a language ℒ) • We have seen how to check basic properties on the reachability graph (and that SCC can be useful) • What if we want to check more general properties? User-Defined Properties • present before (we should see an 푎 before the first 푏) the latch must be locked before take-off • infinitely often (something will always happen, ≠ 퐴푙푤푎푦푠) the timer should always be triggered • leadsto (after every occurrence of 푎 there should be a 푏) there is an audible signal after the alarm is activated • … see example of specification patterns here [Dwyer] Model-Checking System + Requirements informal Description Description M of the of the 휙 behavior property operational denotational formalization verification Does 푀 ⊨ 휙 Does 푀 ≡ 퐺휙 yes / no / c.
    [Show full text]
  • Model Checking Software in Cyberphysical Systems
    Model Checking Software in Cyberphysical Systems Marjan Sirjani Ehsan Khamespanah Edward A. Lee School of IDT ECE Department Department of EECS Mälardalen University University of Tehran UC Berkeley Västerås, Sweden Tehran, Iran Berkeley, USA [email protected] [email protected] [email protected] Abstract—Model checking a software system is about verifying where software reads sensor data and issues commands to that the state trajectory of every execution of the software satisfies physical actuators, ignoring this relationship is more dangerous. formally specified properties. The set of possible executions is For CPS, verification is ultimately about assuring properties modeled as a transition system. Each “state” in the transition system represents an assignment of values to variables, and a state of the physical world not the software abstraction. This means trajectory (a path through the transition system) is a sequence that it is not sufficient to study the software alone. We need of such assignments. For cyberphysical systems (CPSs), however, to also study its interactions with its environment. we are more interested in the state of the physical system than Of course, there is nothing new about formally studying the values of the software variables. The value of model checking the interactions of software with its environment. In 1977, for the software therefore depends on the relationship between the state of the software and the state of the physical system. This example, Pnueli was developing temporal logics for reactive relationship can be complex because of the real-time nature of systems [1]. In 1985, Harel and Pnueli singled out reactive the physical plant, the sensors and actuators, and the software systems as being “particularly problematic when it comes to that is almost always concurrent and distributed.
    [Show full text]
  • Model Checking TLA+ Specifications
    Model Checking TLA+ Specifications Yuan Yu, Panagiotis Manolios, and Leslie Lamport 25 June 1999 Appeared in Correct Hardware Design and Verifica- tion Methods (CHARME ’99), Laurence Pierre and Thomas Kropf editors. Lecture Notes in Computer Sci- ence, number 1703, Springer-Verlag, (September 1999) 54–66. Table of Contents 1 Introduction 54 2TLA+ 57 3CheckingModelsofaTLA+ Specification 58 4 How TLC Works 60 5 Representing States 62 6 Using Disk 63 7 Experimental Results 64 8 Status and Future Work 64 Model Checking TLA+ Specifications Yuan Yu1, Panagiotis Manolios2, and Leslie Lamport1 1 Compaq Systems Research Center [email protected], [email protected] 2 Department of Computer Sciences, University of Texas at Austin [email protected] Abstract. TLA+ is a specification language for concurrent and reactive systems that combines the temporal logic TLA with full first-order logic and ZF set theory. TLC is a new model checker for debugging a TLA+ specification by checking invariance properties of a finite-state model of the specification. It accepts a subclass of TLA+ specifications that should include most descriptions of real system designs. It has been used by engineers to find errors in the cache coherence protocol for a new Compaq multiprocessor. We describe TLA+ specifications and their TLC models, how TLC works, and our experience using it. 1 Introduction Model checkers are usually judged by the size of system they can handle and the class of properties they can check [3, 16, 4]. The system is generally described in either a hardware-description language or a language tailored to the needs of the model checker.
    [Show full text]
  • Model Checking with Mbeddr
    Model Checking for State Machines with mbeddr and NuSMV 1 Abstract State machines are a powerful tool for modelling software. Particularly in the field of embedded software development where parts of a system can be abstracted as state machine. Temporal logic languages can be used to formulate desired behaviour of a state machine. NuSMV allows to automatically proof whether a state machine complies with properties given as temporal logic formulas. mbedder is an integrated development environment for the C programming language. It enhances C with a special syntax for state machines. Furthermore, it can automatically translate the code into the input language for NuSMV. Thus, it is possible to make use of state-of-the-art mathematical proofing technologies without the need of error prone and time consuming manual translation. This paper gives an introduction to the subject of model checking state machines and how it can be done with mbeddr. It starts with an explanation of temporal logic languages. Afterwards, some features of mbeddr regarding state machines and their verification are discussed, followed by a short description of how NuSMV works. Author: Christoph Rosenberger Supervising Tutor: Peter Sommerlad Lecture: Seminar Program Analysis and Transformation Term: Spring 2013 School: HSR, Hochschule für Technik Rapperswil Model Checking with mbeddr 2 Introduction Model checking In the words of Cavada et al.: „The main purpose of a model checker is to verify that a model satisfies a set of desired properties specified by the user.” [1] mbeddr As Ratiu et al. state in their paper “Language Engineering as an Enabler for Incrementally Defined Formal Analyses” [2], the semantic gap between general purpose programming languages and input languages for formal verification tools is too big.
    [Show full text]
  • Model Checking Accomplishments and Opportunities
    Model Checking Accomplishments and Opportunities Rajeev Alur Systems Design Research Lab University of Pennsylvania www.cis.upenn.edu/~alur/ Debugging Tools q Program Analysis Type systems, pointer analysis, data-flow analysis q Simulation Effective in discovering bugs in early stages q Testing Expensive! q Formal Verification Mathematical proofs, Not yet practical Quest for Better Debugging q Bugs are expensive! Pentium floating point bug, Arian-V disaster q Testing is expensive! More time than design and implementation q Safety critical applications Certification mandated model yes temporal Model Checker property error-trace Advantages Automated formal verification, Effective debugging tool Moderate industrial success In-house groups: Intel, Microsoft, Lucent, Motorola… Commercial model checkers: FormalCheck by Cadence Obstacles Scalability is still a problem (about 100 state vars) Effective use requires great expertise Cache consistency: Gigamax Real design of a distributed multiprocessor Global bus UIC UIC UIC Cluster bus M P M P Read-shared/read-owned/write-invalid/write-shared/… Deadlock found using SMV Similar successes: IEEE Futurebus+ standard, network RFCs Talk Outline ü Introduction Ü Foundations q MOCHA q Current Trends and Future Components of a Model Checker q Modeling language Concurrency, non-determinism, simple data types q Requirements language Invariants, deadlocks, temporal logics q Search algorithms Enumerative vs symbolic + many optimizations q Debugging feedback Reachability Problem Model variables X ={x1, … xn} Each var is of finite type, say, boolean Initialization: I(X) condition over X Update: T(X,X’) How new vars X’ are related to old vars X as a result of executing one step of the program Target set: F(X) Computational problem: Can F be satisfied starting with I by repeatedly applying T ? Graph Search problem Symbolic Solution Data type: region to represent state-sets R:=I(X) Repeat If R intersects T report “yes” Else if R contains Post(R) report “no” Else R := R union Post(R) Post(R(X))= (Exists X.
    [Show full text]